Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials | Paper Citation Record

Observation 22365133-cb98-40db-a82f-c7d2f794427e · outbound

This paper cites A review of extended/generalized finite element methods for material modeling.Modelling and Simulation in Materials Science and Engineering.2009;17(4):043001.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials A review of extended/generalized finite element methods for material modeling.Modelling and Simulation in Materials Science and Engineering.2009;17(4):043001

Reference 1

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This paper cites The variational approach to fracture.Journal of Elasticity.2008;91(1-3):5–148.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials The variational approach to fracture.Journal of Elasticity.2008;91(1-3):5–148

Reference 2

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This paper cites Phase-field material point method for brittle fracture.International Journal for Numerical Methods in Engineering.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials Phase-field material point method for brittle fracture.International Journal for Numerical Methods in Engineering

Reference 3

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Observation 157eb197-afda-46a6-9b24-bb69c32756ea · outbound

This paper cites Phase-field modeling of brittle fracture using an efficient virtual element scheme.Computer Methods in Applied Mechanics and Engineering.2018;341:443–466.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials Phase-field modeling of brittle fracture using an efficient virtual element scheme.Computer Methods in Applied Mechanics and Engineering.2018;341:443–466

Reference 4

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Observation 5727465b-6f5c-4ae8-b25e-c4a994cc9f1b · outbound

This paper cites Adaptive phase-field modeling of brittle fracture using the scaled boundary finite element method.Computer Methods in Applied Mechanics and Engineering.2019;355:284–307.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials Adaptive phase-field modeling of brittle fracture using the scaled boundary finite element method.Computer Methods in Applied Mechanics and Engineering.2019;355:284–307

Reference 5

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Observation 67bc10d4-efea-4f2b-9579-187d0958daa0 · outbound

This paper cites Extension of high-fidelity time-domain spectral element formulation for phase-field modeling of fracture: A static analysis.Engineering Fracture Mechanics.2025;317:110908.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials Extension of high-fidelity time-domain spectral element formulation for phase-field modeling of fracture: A static analysis.Engineering Fracture Mechanics.2025;317:110908

Reference 6

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This paper cites A review on phase-field models of brittle fracture and a new fast hybrid formulation.Computational Mechanics.2015;55(2):383–405.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials A review on phase-field models of brittle fracture and a new fast hybrid formulation.Computational Mechanics.2015;55(2):383–405

Reference 7

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Observation 8c352c28-7ed2-4855-9fec-d96347a26812 · outbound

This paper cites Gradient damagevsphase-field approaches for fracture: Similarities and differences.Computer Methods in Applied Mechanics and Engineering.2016;312:78–94.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials Gradient damagevsphase-field approaches for fracture: Similarities and differences.Computer Methods in Applied Mechanics and Engineering.2016;312:78–94

Reference 8

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Observation a42d1fd3-ccc5-44ba-8f41-d5c265974445 · outbound

This paper cites Crack nucleation in variational phase-field models of brittle fracture.Journal of the Mechanics and Physics of Solids.2018;110:80–99.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials Crack nucleation in variational phase-field models of brittle fracture.Journal of the Mechanics and Physics of Solids.2018;110:80–99

Reference 9

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This paper cites A FEniCS implementation of the phase field method for quasi-static brittle fracture.Frontiers of Structural and Civil Engineering.2019;13(2):380–396.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials A FEniCS implementation of the phase field method for quasi-static brittle fracture.Frontiers of Structural and Civil Engineering.2019;13(2):380–396

Reference 10

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Observation b597751d-eb95-470f-b06c-d3794899312a · outbound

This paper cites GPFniCS: A generalised phase field method to model fracture.SoftwareX.2023;24:101594.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials GPFniCS: A generalised phase field method to model fracture.SoftwareX.2023;24:101594

Reference 11

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This paper cites An open-source moose implementation of phase-field modeling of fracture in functionally graded materials.Procedia Structural Integrity.2024;58:115–121.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials An open-source moose implementation of phase-field modeling of fracture in functionally graded materials.Procedia Structural Integrity.2024;58:115–121

Reference 12

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Observation b9d3f9ee-b751-465f-acf6-726e0ee1d3ac · outbound

This paper cites PhaseFieldX: An Open-Source Framework for Advanced Phase-Field Simulations.Journal of Open Source Software.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials PhaseFieldX: An Open-Source Framework for Advanced Phase-Field Simulations.Journal of Open Source Software

Reference 13

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Observation aa06030d-7815-43c9-a38e-4368cc65534d · outbound

This paper cites PhaFiDyn: An explicit dynamic phase field damage model implementation.SoftwareX.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials PhaFiDyn: An explicit dynamic phase field damage model implementation.SoftwareX

Reference 14

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Observation b8d0f100-b3fc-4d24-ac45-1dce72ec08fe · outbound

This paper cites A detailed guide to an open-source implementation of the hybrid phase field method for 3D fracture modeling in deal.II.Computer Physics Communications.2026;319:109901.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials A detailed guide to an open-source implementation of the hybrid phase field method for 3D fracture modeling in deal.II.Computer Physics Communications.2026;319:109901

Reference 15

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Observation 2506439b-844b-4a41-9b23-4d34006e061b · outbound

This paper cites A phase-field description of dynamic brittle fracture.Computer Methods in Applied Mechanics and Engineering.2012;217-220:77–95.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials A phase-field description of dynamic brittle fracture.Computer Methods in Applied Mechanics and Engineering.2012;217-220:77–95

Reference 16

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Observation b95fc244-77e8-4d3b-a9d1-cfb441b376b9 · outbound

This paper cites An explicit phase field method for brittle dynamic fracture.Computers & Structures.2019;217:45–56.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials An explicit phase field method for brittle dynamic fracture.Computers & Structures.2019;217:45–56

Reference 17

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Observation 778f231c-eb34-42da-8474-30d29ea1943d · outbound

This paper cites Evaluation of variational phase-field models for dynamic brittle fracture.Engineering Fracture Mechanics.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials Evaluation of variational phase-field models for dynamic brittle fracture.Engineering Fracture Mechanics

Reference 18

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This paper cites Phase-field cohesive fracture theory: A unified framework for dissipative systems based on variational inequality of virtual works.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials Phase-field cohesive fracture theory: A unified framework for dissipative systems based on variational inequality of virtual works

Reference 19

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Observation 0ca26b6d-6c55-4bf8-b670-5800b074eb7d · outbound

This paper cites Multi-phase-field modeling of anisotropic crack propagation for polycrystalline materials.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials Multi-phase-field modeling of anisotropic crack propagation for polycrystalline materials

Reference 20

Resolution: verified exact; doi, observed 2026-08-01T08:29:22.260039Z

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Observation 855254d1-ff05-48dc-ae80-c9e51f1be359 · outbound

This paper cites Phase-field modeling of anisotropic brittle fracture including several damage mechanisms.Computer Methods in Applied Mechanics and Engineering.2018;336:213–236.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials Phase-field modeling of anisotropic brittle fracture including several damage mechanisms.Computer Methods in Applied Mechanics and Engineering.2018;336:213–236

Reference 21

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Observation 08243071-1ded-4765-a3a9-059eb9531751 · outbound

This paper cites Crack kinking in a variational phase-field model of brittle fracture with strongly anisotropic surface energy.Journal of the Mechanics and Physics of Solids.2019;125:502–522.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials Crack kinking in a variational phase-field model of brittle fracture with strongly anisotropic surface energy.Journal of the Mechanics and Physics of Solids.2019;125:502–522

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Observation 6ec7ede9-b074-4fdb-8e58-b59ef9c68ce5 · outbound

This paper cites Phase field modeling of anisotropic silicon crystalline cracking in 3D thin-walled photovoltaic laminates.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials Phase field modeling of anisotropic silicon crystalline cracking in 3D thin-walled photovoltaic laminates

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Observation 38c0a6c9-f0d8-4b67-b889-71e1a164812b · outbound

This paper cites Phase-field modeling of anisotropic fracture of additively manufactured parts.Engineering Fracture Mechanics.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials Phase-field modeling of anisotropic fracture of additively manufactured parts.Engineering Fracture Mechanics

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Observation 8f586720-fc94-44e1-9f8d-e6bd2f28e336 · outbound

This paper cites A phase-field model for fatigue crack growth.Journal of the Mechanics and Physics of Solids.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials A phase-field model for fatigue crack growth.Journal of the Mechanics and Physics of Solids

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Observation 57416065-23a0-4fb6-afa1-dfe56645fa41 · outbound

This paper cites A framework to model the fatigue behavior of brittle materials based on a variational phase-field approach.Computer Methods in Applied Mechanics and Engineering.2020;361:112731.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials A framework to model the fatigue behavior of brittle materials based on a variational phase-field approach.Computer Methods in Applied Mechanics and Engineering.2020;361:112731

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Observation 54a47a8f-f4b0-4a53-a279-f00e1e79185e · outbound

This paper cites An acceleration scheme for the phase field fatigue fracture simulation with a concurrent temporal homogenization method.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials An acceleration scheme for the phase field fatigue fracture simulation with a concurrent temporal homogenization method

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Observation ee59f935-e531-4c43-9f03-e8711382aad2 · outbound

This paper cites A review on phase field models for fracture and fatigue.Engineering Fracture Mechanics.2023;289:109419.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials A review on phase field models for fracture and fatigue.Engineering Fracture Mechanics.2023;289:109419

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Observation 71decbba-d22d-4a98-a153-67f97e2238c2 · outbound

This paper cites A Crystal Plasticity Phase-Field Study on the Effects of Grain Boundary Degradation on the Fatigue Behavior of a Nickel-Based Superalloy.Materials.2025;18(14):3309.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials A Crystal Plasticity Phase-Field Study on the Effects of Grain Boundary Degradation on the Fatigue Behavior of a Nickel-Based Superalloy.Materials.2025;18(14):3309

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This paper cites A generalised, multi-phase-field theory for dissolution-driven stress corrosion cracking and hydrogen embrittlement.Journal of the Mechanics and Physics of Solids.2022;166:104951.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials A generalised, multi-phase-field theory for dissolution-driven stress corrosion cracking and hydrogen embrittlement.Journal of the Mechanics and Physics of Solids.2022;166:104951

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This paper cites Numerical Simulation for Hydrogen-Assisted Cracking: An Explicit Phase-Field Formulation.Materials.2023;16(4):1708.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials Numerical Simulation for Hydrogen-Assisted Cracking: An Explicit Phase-Field Formulation.Materials.2023;16(4):1708

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Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials Unresolved cited work

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Observation ba3b32ad-11f7-42d5-86d6-49c0c6c3e7cd · outbound

This paper cites A Continuous Damage Mechanics Model for Ductile Fracture.Journal of Engineering Materials and Technology.1985;107(1):83–89.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials A Continuous Damage Mechanics Model for Ductile Fracture.Journal of Engineering Materials and Technology.1985;107(1):83–89

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Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials Unresolved cited work

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Observation e4faa0db-18b2-4bc6-b966-98a2cbe4d27f · outbound

This paper cites Analysis of the cup-cone fracture in a round tensile bar.Acta Metallurgica.1984;32(1):157–169.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials Analysis of the cup-cone fracture in a round tensile bar.Acta Metallurgica.1984;32(1):157–169

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This paper cites An Experimental Study of the Polycrystalline Plasticity of Austenitic Stainless Steel.International Journal of Plasticity.2015;74.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials An Experimental Study of the Polycrystalline Plasticity of Austenitic Stainless Steel.International Journal of Plasticity.2015;74

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This paper cites An experimental study of the polycrystalline plasticity of lamellar titanium aluminide.International Journal of Plasticity.2019;118.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials An experimental study of the polycrystalline plasticity of lamellar titanium aluminide.International Journal of Plasticity.2019;118

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Observation f3e130a5-f695-4749-a828-4e92bef526d3 · outbound

This paper cites Reduced partitioning of plastic strain for strong and yet ductile precipitate-strengthened alloys.Scientific Reports.2018;8(1):8698.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials Reduced partitioning of plastic strain for strong and yet ductile precipitate-strengthened alloys.Scientific Reports.2018;8(1):8698

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Observation 6c84e93a-7baf-4cfc-a7c4-f256fe5ed5c4 · outbound

This paper cites Phase field modeling of ductile fracture at finite strains: A variational gradient-extended plasticity-damage theory.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials Phase field modeling of ductile fracture at finite strains: A variational gradient-extended plasticity-damage theory

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Observation 0db87b30-569c-4ed9-b9a7-f283ffe69ffd · outbound

This paper cites Phase-field modeling of ductile fracture.Computational Mechanics.2015;55:1013–1040.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials Phase-field modeling of ductile fracture.Computational Mechanics.2015;55:1013–1040

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Observation 12debffc-785c-4d11-8195-2074fad19a2f · outbound

This paper cites A phase-field/gradient damage model for brittle fracture in elastic–plastic solids.International Journal of Plasticity.2015;65:269–296.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials A phase-field/gradient damage model for brittle fracture in elastic–plastic solids.International Journal of Plasticity.2015;65:269–296

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This paper cites Crack phase-field model equipped with plastic driving force and degrading fracture toughness for ductile fracture simulation.Computational Mechanics.2022;69(1):151–175.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials Crack phase-field model equipped with plastic driving force and degrading fracture toughness for ductile fracture simulation.Computational Mechanics.2022;69(1):151–175

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Observation ba2b1390-9c6c-49d1-a5e6-18ee0afe3821 · outbound

This paper cites Attaining regularization length insensitivity in phase-field models of ductile failure.Computer Methods in Applied Mechanics and Engineering.2021;384:113936.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials Attaining regularization length insensitivity in phase-field models of ductile failure.Computer Methods in Applied Mechanics and Engineering.2021;384:113936

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Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials Unresolved cited work

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This paper cites A Micropolar Phase Field Fracture Model for Elastoplastic Solids Applied to Concrete Failure.International Journal for Numerical Methods in Engineering.2025;126(19):e70140.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials A Micropolar Phase Field Fracture Model for Elastoplastic Solids Applied to Concrete Failure.International Journal for Numerical Methods in Engineering.2025;126(19):e70140

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Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials Unresolved cited work

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Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials Unresolved cited work

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Observation 98c266ca-de92-4a3d-bc6e-91901b8511e6 · outbound

This paper cites 3D micromechanical progressive failure simulation for fiber-reinforced composites.Composite Structures.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials 3D micromechanical progressive failure simulation for fiber-reinforced composites.Composite Structures

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Observation 7c875443-5c9c-4985-b6ec-9f3b9ef4bd1d · outbound

This paper cites an unresolved cited work.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials Unresolved cited work

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Resolution: unresolved; no resolver link, observed 2026-08-01T08:26:05.242740Z

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Observation 1e87abef-ac47-4da6-adf2-fc91b618e651 · outbound

This paper cites dD, Lim H.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials dD, Lim H

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Resolution: unresolved; no resolver link, observed 2026-08-01T08:26:05.356978Z

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Observation e42939fb-3b25-478b-98f7-5775068d44cf · outbound

This paper cites an unresolved cited work.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials Unresolved cited work

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Resolution: unresolved; no resolver link, observed 2026-08-01T08:26:05.470964Z

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Observation 2dc7cd63-863e-408a-a00a-20d4e076198e · outbound

This paper cites Matrix-free multigrid solvers for phase-field fracture problems.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials Matrix-free multigrid solvers for phase-field fracture problems

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Resolution: unresolved; no resolver link, observed 2026-08-01T08:26:05.583008Z

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Observation 05984a81-528f-4e3b-a166-d46e7c52768e · outbound

This paper cites A matrix-free approach for finite-strain hyperelastic problems using geometric multigrid.International Journal for Numerical Methods in Engineering.2020;121(6):1224–1248.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials A matrix-free approach for finite-strain hyperelastic problems using geometric multigrid.International Journal for Numerical Methods in Engineering.2020;121(6):1224–1248

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Resolution: unresolved; no resolver link, observed 2026-08-01T08:26:05.700005Z

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Observation 3bc226cb-3f70-4932-b9f0-6d181eaa57ef · outbound

This paper cites Performance Portable Solid Mechanics via Matrix-Free $p$-Multigrid.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials Performance Portable Solid Mechanics via Matrix-Free $p$-Multigrid

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Resolution: unresolved; no resolver link, observed 2026-08-01T08:26:05.796952Z

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Observation 4319eb6c-0364-4009-b27b-7006307dd8ff · outbound

This paper cites Matrix-free higher-order finite element methods for hyperelasticity.Computer Methods in Applied Mechanics and Engineering.2025;435:117600.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials Matrix-free higher-order finite element methods for hyperelasticity.Computer Methods in Applied Mechanics and Engineering.2025;435:117600

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Resolution: unresolved; no resolver link, observed 2026-08-01T08:26:05.911996Z

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Observation 66bd24a1-c72c-4633-b2f5-ad43cbf2ee66 · outbound

This paper cites Parallel matrix-free higher-order finite element solvers for phase-field fracture problems.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials Parallel matrix-free higher-order finite element solvers for phase-field fracture problems

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Resolution: unresolved; no resolver link, observed 2026-08-01T08:26:06.011661Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2d9367cf-e60b-4f45-9a01-2f7c13d772fe · outbound

This paper cites an unresolved cited work.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials Unresolved cited work

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Resolution: unresolved; no resolver link, observed 2026-08-01T08:26:06.111808Z

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Unavailable: canonical work link unavailable.

Observation 84188aae-3c73-4be0-a4fd-6a4ca7bcf8fa · outbound

This paper cites Matrix-Free Geometric Multigrid Preconditioning of Combined Newton-GMRES for Solving Phase-Field Fracture with Local Mesh Refinement.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials Matrix-Free Geometric Multigrid Preconditioning of Combined Newton-GMRES for Solving Phase-Field Fracture with Local Mesh Refinement

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Resolution: unresolved; no resolver link, observed 2026-08-01T08:26:06.187254Z

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Observation de487f34-06fe-4c2c-9f26-87052b7fcccf · outbound

This paper cites A computational model for generalized inelastic materials at finite strains combining elastic, viscoelastic and plastic material behaviour.Engineering Computations.2003.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials A computational model for generalized inelastic materials at finite strains combining elastic, viscoelastic and plastic material behaviour.Engineering Computations.2003

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Resolution: verified exact; doi, observed 2026-08-01T08:29:20.749001Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 489303f6-62c8-4c7e-b2eb-814db82e38d0 · outbound

This paper cites Ratel: Performance portable solid mechanics with libCEED and PETSc.Journal of Open Source Software.2026;11(118):8388.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials Ratel: Performance portable solid mechanics with libCEED and PETSc.Journal of Open Source Software.2026;11(118):8388

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Resolution: verified exact; doi, observed 2026-08-01T08:29:20.684074Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 8ede74dc-539d-43b1-b6a6-499aa417441e · outbound

This paper cites libCEED: Fast algebra for high-order element-based discretizations.Journal of Open Source Software.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials libCEED: Fast algebra for high-order element-based discretizations.Journal of Open Source Software

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Resolution: verified exact; doi, observed 2026-08-01T08:29:20.604981Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 5b96215a-aa33-4fe7-9ccb-7c3060d39879 · outbound

This paper cites PETSc Users Manual.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials PETSc Users Manual

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Resolution: unresolved; no resolver link, observed 2026-08-01T08:26:06.491188Z

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Observation 010983f0-1ecc-4001-b3bb-9a1a3969fbc8 · outbound

This paper cites A model for finite strain elasto-plasticity based on logarithmic strains: Computational issues.Computer Methods in Applied Mechanics and Engineering.1992;94(1):35–61.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials A model for finite strain elasto-plasticity based on logarithmic strains: Computational issues.Computer Methods in Applied Mechanics and Engineering.1992;94(1):35–61

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Resolution: verified exact; doi, observed 2026-08-01T08:29:20.405531Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 4d8d90e6-1edd-4506-a74b-5afbeddf8061 · outbound

This paper cites Elastic-Plastic Deformation at Finite Strains.Journal of Applied Mechanics.1969;36(1):1–6.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials Elastic-Plastic Deformation at Finite Strains.Journal of Applied Mechanics.1969;36(1):1–6

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Resolution: verified exact; doi, observed 2026-08-01T08:29:20.289746Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 72e6a1e9-2ae0-4f04-8583-8b85dc583b02 · outbound

This paper cites an unresolved cited work.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials Unresolved cited work

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Resolution: unresolved; no resolver link, observed 2026-08-01T08:26:06.738095Z

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Observation d093ab31-79e2-447d-940c-37a92c54b22e · outbound

This paper cites A theory of finite viscoelasticity and numerical aspects.International Journal of Solids and Structures.1998;35(26– 27):3455–3482.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials A theory of finite viscoelasticity and numerical aspects.International Journal of Solids and Structures.1998;35(26– 27):3455–3482

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Resolution: verified exact; doi, observed 2026-08-01T08:29:20.187943Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 98322095-d568-44c6-aece-e1629e15bef9 · outbound

This paper cites an unresolved cited work.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials Unresolved cited work

Reference 67

Resolution: verified exact; doi, observed 2026-08-01T08:29:20.035217Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation a1cc1905-db99-4c7b-927f-8d9714de8ea2 · outbound

This paper cites Finite deformation constitutive equations and a time integration procedure for isotropic, hyperelastic-viscoplastic solids.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials Finite deformation constitutive equations and a time integration procedure for isotropic, hyperelastic-viscoplastic solids

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Resolution: verified exact; doi, observed 2026-08-01T08:29:19.886217Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 0faf339d-da05-4300-837b-6336fe62f0f9 · outbound

This paper cites an unresolved cited work.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials Unresolved cited work

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Resolution: unresolved; no resolver link, observed 2026-08-01T08:26:07.012292Z

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Observation a7be0143-e08e-416a-9d52-5bea1f0f473a · outbound

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Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials Stable numerics for finite-strain elasticity.International Journal for Numerical Methods in Engineering.2024:e7563

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Resolution: verified exact; doi, observed 2026-08-01T08:29:19.723720Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 2dab387b-6497-45c6-9a58-920e61c7b629 · outbound

This paper cites A variational formulation of constitutive models and updates in non-linear finite viscoelasticity.International Journal for Numerical Methods in Engineering.2006;65(11):1831–1864.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials A variational formulation of constitutive models and updates in non-linear finite viscoelasticity.International Journal for Numerical Methods in Engineering.2006;65(11):1831–1864

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Resolution: verified exact; doi, observed 2026-08-01T08:29:19.570734Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation e4ece3e9-b484-4463-941e-e1f87f1fe7c1 · outbound

This paper cites Regularized formulation of the variational brittle fracture with unilateral contact: Numerical experiments.Journal of the Mechanics and Physics of Solids.2009;57(8):1209–1229.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials Regularized formulation of the variational brittle fracture with unilateral contact: Numerical experiments.Journal of the Mechanics and Physics of Solids.2009;57(8):1209–1229

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Resolution: unresolved; no resolver link, observed 2026-08-01T08:26:07.242597Z

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Observation 654c8351-df82-4eb9-a192-5d6ddd16107f · outbound

This paper cites On the ductile enlargement of voids in triaxial stress fields*.Journal of the Mechanics and Physics of Solids.1969;17(3):201–.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials On the ductile enlargement of voids in triaxial stress fields*.Journal of the Mechanics and Physics of Solids.1969;17(3):201–

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Resolution: unresolved; no resolver link, observed 2026-08-01T08:26:07.319077Z

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Unavailable: canonical work link unavailable.

Observation 6fceac4f-0396-495a-b95b-86c53c7dc530 · outbound

This paper cites On degradation functions in phase field fracture models.Computational Materials Science.2015;108:374–384.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials On degradation functions in phase field fracture models.Computational Materials Science.2015;108:374–384

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Resolution: unresolved; no resolver link, observed 2026-08-01T08:26:07.475456Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8112904e-728d-4e73-b9ef-0a48a3c117af · outbound

This paper cites an unresolved cited work.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials Unresolved cited work

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Resolution: unresolved; no resolver link, observed 2026-08-01T08:26:07.553446Z

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Unavailable: canonical work link unavailable.

Observation 141356f3-b326-4aec-aa54-713cdd9d391b · outbound

This paper cites A fracture-controlled path-following technique for phase-field modeling of brittle fracture.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials A fracture-controlled path-following technique for phase-field modeling of brittle fracture

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Resolution: verified exact; doi, observed 2026-08-01T08:29:19.370967Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 5a258d60-6b36-4bea-9a69-dabb03771577 · outbound

This paper cites an unresolved cited work.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials Unresolved cited work

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Resolution: unresolved; no resolver link, observed 2026-08-01T08:26:07.683603Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7b09057a-69dd-4771-af35-9b2ed3c807cf · outbound

This paper cites How regularization concepts interfere with (quasi-)brittle damage: a comparison based on a unified variational framework.Continuum Mechanics and Thermodynamics.2022;34(6):1517–1544.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials How regularization concepts interfere with (quasi-)brittle damage: a comparison based on a unified variational framework.Continuum Mechanics and Thermodynamics.2022;34(6):1517–1544

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Resolution: unresolved; no resolver link, observed 2026-08-01T08:26:07.786127Z

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Unavailable: canonical work link unavailable.

Observation 267b7bcf-7ab5-46a7-bcdf-6b068377178a · outbound

This paper cites A "missing" family of classical orthogonal polynomials.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials A "missing" family of classical orthogonal polynomials

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Resolution: unresolved; no resolver link, observed 2026-08-01T08:26:07.858728Z

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Unavailable: canonical work link unavailable.

Observation ad80e15a-5170-41f1-8ede-bee08243a8b0 · outbound

This paper cites A line search assisted monolithic approach for phase-field computing of brittle fracture.Computer Methods in Applied Mechanics and Engineering.2016;312:276–303.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials A line search assisted monolithic approach for phase-field computing of brittle fracture.Computer Methods in Applied Mechanics and Engineering.2016;312:276–303

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Resolution: unresolved; no resolver link, observed 2026-08-01T08:26:07.966460Z

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Observation 0fc93419-3355-4459-8185-c50513611b84 · outbound

This paper cites Phase field fracture modelling using quasi-Newton methods and a new adaptive step scheme.Theoretical and Applied Fracture Mechanics.2020;107:102446.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials Phase field fracture modelling using quasi-Newton methods and a new adaptive step scheme.Theoretical and Applied Fracture Mechanics.2020;107:102446

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Resolution: unresolved; no resolver link, observed 2026-08-01T08:26:08.082328Z

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Observation facf1a8a-7756-4966-be52-825b3826137e · outbound

This paper cites In Situ Imaging during Compression of Plastic Bonded Explosives for Damage Modeling.Materials.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials In Situ Imaging during Compression of Plastic Bonded Explosives for Damage Modeling.Materials

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Resolution: verified exact; doi, observed 2026-08-01T08:29:19.264091Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 71b37a34-c82d-402e-85f5-983e5b883169 · outbound

This paper cites In-Situ Internal Deformation Measurement of an IDOX Particulate Estane Binder Composite via Backward Digital V olume Correlation.Experimental Mechanics.2026;66(1):103–119.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials In-Situ Internal Deformation Measurement of an IDOX Particulate Estane Binder Composite via Backward Digital V olume Correlation.Experimental Mechanics.2026;66(1):103–119

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Resolution: verified exact; doi, observed 2026-08-01T08:29:19.092911Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation a7df3c7f-a9be-476e-b933-337d3ae47a55 · outbound

This paper cites MicroStructPy: A statistical microstructure mesh generator in Python.SoftwareX.2020;12:100595.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials MicroStructPy: A statistical microstructure mesh generator in Python.SoftwareX.2020;12:100595

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Resolution: unresolved; no resolver link, observed 2026-08-01T08:26:08.324396Z

Source-reported events for the cited work

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Observation 808ecb78-9ebe-4552-ab35-72ea76acb941 · outbound

This paper cites an unresolved cited work.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials Unresolved cited work

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Resolution: unresolved; no resolver link, observed 2026-08-01T08:26:08.390548Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation dfa21872-18b4-4744-b730-5b8abea8cb32 · outbound

This paper cites Gmsh: A 3-D finite element mesh generator with built-in pre- and post-processing facilities.International Journal for Numerical Methods in Engineering.2009;79(11):1309–1331.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials Gmsh: A 3-D finite element mesh generator with built-in pre- and post-processing facilities.International Journal for Numerical Methods in Engineering.2009;79(11):1309–1331

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Resolution: unresolved; no resolver link, observed 2026-08-01T08:26:08.464808Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 799f4ff8-4e37-48fe-8378-412183633cf8 · outbound

This paper cites NETGEN—An advancing front 2D/3D-mesh generator based on abstract rules.Computing and Visualization in Science.1997;1(1):41–.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials NETGEN—An advancing front 2D/3D-mesh generator based on abstract rules.Computing and Visualization in Science.1997;1(1):41–

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Resolution: unresolved; no resolver link, observed 2026-08-01T08:26:08.531765Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 77ddd925-13e3-417a-9e3d-80b07ff4639b · outbound

This paper cites micromorph / STLs postprocessing for 3Dmeshing of composites · GitLab.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials micromorph / STLs postprocessing for 3Dmeshing of composites · GitLab

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Resolution: unresolved; no resolver link, observed 2026-08-01T08:26:08.662632Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation aed40a56-51e1-4db2-b20f-25fa3634469e · outbound

This paper cites an unresolved cited work.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials Unresolved cited work

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Resolution: unresolved; no resolver link, observed 2026-08-01T08:26:08.596441Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 484490d9-c844-4e17-b861-2d59219d104c · outbound

This paper cites hypre: A Library of High Performance Preconditioners.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials hypre: A Library of High Performance Preconditioners

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Resolution: unresolved; no resolver link, observed 2026-08-01T08:26:08.794580Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e30c2032-7393-4a48-8d9e-c5c57f075eda · outbound

This paper cites micromorph / Synthetic composite · GitLab.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials micromorph / Synthetic composite · GitLab

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Resolution: unresolved; no resolver link, observed 2026-08-01T08:26:08.731579Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f50dcb22-4ebb-40b9-858a-5d28ca7f25f9 · outbound

This paper cites Kokkos 3: Programming Model Extensions for the Exascale Era.IEEE Transactions on Parallel and Distributed Systems.2022;33(4):805–817.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials Kokkos 3: Programming Model Extensions for the Exascale Era.IEEE Transactions on Parallel and Distributed Systems.2022;33(4):805–817

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Resolution: unresolved; no resolver link, observed 2026-08-01T08:26:08.970817Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c42e20dd-2076-4f04-a4b9-a79a7914728d · outbound

This paper cites PETSc/TAO developments for GPU-based early exascale systems.The International Journal of High Performance Computing Applications.2025;39(2):306–325.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials PETSc/TAO developments for GPU-based early exascale systems.The International Journal of High Performance Computing Applications.2025;39(2):306–325

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Resolution: verified exact; doi, observed 2026-08-01T08:29:18.956290Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation ac67f5d8-c23b-44a8-9892-8a709d9cdee0 · outbound

This paper cites A new mechanism of strain transfer in polycrystals.Scientific Reports.2020;10(1).

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials A new mechanism of strain transfer in polycrystals.Scientific Reports.2020;10(1)

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Resolution: verified exact; doi, observed 2026-08-01T08:29:18.688219Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 65f22fa8-f698-49f6-8309-46f92730db08 · outbound

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Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials Calibrating a finite-strain phase-field model of fracture for bonded granular materials with uncertainty quantification.Journal of Applied Physics.2025;138(23):234903

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Resolution: verified exact; doi, observed 2026-08-01T08:29:18.802360Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 50dd1a8b-665c-487c-a3b1-bd76b02b635d · outbound

This paper cites Strain gradient crystal plasticity: size-dependentdeformation of bicrystals.Journal of the Mechanics and Physics of Solids.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials Strain gradient crystal plasticity: size-dependentdeformation of bicrystals.Journal of the Mechanics and Physics of Solids

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Resolution: verified exact; doi, observed 2026-08-01T08:29:18.526237Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation c419fe9b-192b-446f-8986-b8173b13a864 · outbound

This paper cites Crystallographic aspects of geometrically-necessary and statistically-stored dislocation density.Acta Materialia.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials Crystallographic aspects of geometrically-necessary and statistically-stored dislocation density.Acta Materialia

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Resolution: verified exact; doi, observed 2026-08-01T08:29:18.628873Z

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Observation 6d9c73c1-5cdf-4556-953a-5b6dd69a54c3 · outbound

This paper cites Ratel iMPM: A Performance-Portable, Matrix-Free Implicit Material Point Method for Exascale Systems.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials Ratel iMPM: A Performance-Portable, Matrix-Free Implicit Material Point Method for Exascale Systems

Reference 98

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Observation eb19a4c1-028a-49b2-a8bc-7d435962a439 · outbound

This paper cites Lattice incompatibility and a gradient theory of crystal plasticity.Journal of the Mechanics and Physics of Solids.2000;48(8):1565–1595.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials Lattice incompatibility and a gradient theory of crystal plasticity.Journal of the Mechanics and Physics of Solids.2000;48(8):1565–1595

Reference 99

Resolution: verified exact; doi, observed 2026-08-01T08:29:18.463619Z

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Observation c36acd9f-07ab-488b-9f10-e4230875093b · outbound

This paper cites an unresolved cited work.

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials Unresolved cited work

Reference 217

Resolution: verified exact; doi, observed 2026-08-01T08:29:19.490110Z

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